A Model of Search with Two Stages of Information Acquisition and Additive Learning

This paper presents a model of choice with two stages of information acquisition. In this model, the choice problem can be interpreted as a variant of a more general multiarmed bandit problem. We assume that information acquisition takes a simple “additive form”—the value of an alternative is the sum of two components, which the decision maker can learn by undertaking two stages of information acquisition. This assumption yields a model that is tractable for the purposes of structural estimation. One possible application of the model is to online purchasing on e-commerce sites. For a consumer on an e-commerce website, there are potentially two stages of information acquisition: the consumer can obtain information about an alternative from (i) browsing the search results page and (ii) clicking on the alternative. By way of contrast, in much of the literature on structural econometric models of online purchasing, there is typically only one stage of information acquisition. Our paper may, therefore, provide a more realistic theory for modeling search, at least for those types of search—such as online purchasing—that involve two stages of information acquisition. This paper was accepted by Manel Baucells, behavioral economics and decision analysis.

Multiplicative Parameterization Above a Guarantee

Parameterization above a guarantee is a successful paradigm in Parameterized Complexity. To the best of our knowledge, all fixed-parameter tractable problems in this paradigm share an additive form defined as follows. Given an instance ( I,k ) of some (parameterized) problem π with a guarantee g(I) , decide whether I admits a solution of size at least (or at most) k + g(I) . Here, g(I) is usually a lower bound on the minimum size of a solution. Since its introduction in 1999 for M AX SAT and M AX C UT (with g(I) being half the number of clauses and half the number of edges, respectively, in the input), analysis of parameterization above a guarantee has become a very active and fruitful topic of research. We highlight a multiplicative form of parameterization above (or, rather, times) a guarantee: Given an instance ( I,k ) of some (parameterized) problem π with a guarantee g(I) , decide whether I admits a solution of size at least (or at most) k · g(I) . In particular, we study the Long Cycle problem with a multiplicative parameterization above the girth g(I) of the input graph, which is the most natural guarantee for this problem, and provide a fixed-parameter algorithm. Apart from being of independent interest, this exemplifies how parameterization above a multiplicative guarantee can arise naturally. We also show that, for any fixed constant ε > 0, multiplicative parameterization above g(I) 1+ε of Long Cycle yields para-NP-hardness, thus our parameterization is tight in this sense. We complement our main result with the design (or refutation of the existence) of fixed-parameter algorithms as well as kernelization algorithms for additional problems parameterized multiplicatively above girth.

Modeling and Use of Inter-Criteria Decision Analysis for Selecting Growth Rate Models for Batch Cultivation of Yeast Kluyveromyces marxianus var. lactis MC 5

Ten unstructured models of Monod, Mink, Tessier, Moser, Aiba, Andrews, Haldane, Luong, Edward, and Han-Levenspiel are considered in this paper to explain the kinetics of cell growth for batch cultivation of the yeast Kluyweromyces marxianus var. lactis MC 5. For the first time, two independent kinetic models are used to model the process for the two basic substrates—lactose and oxygen. The selection of the most appropriate growth rate models has been made through a new multi-criteria decision-making approach called the Inter-Criteria Decision Analysis (ICDA) method. The application of ICDA to the growth rate of lactose and oxygen alone has shown that there have been many correlations between the studied models. Thus, the models for the growth rate, depending only on lactose, are reduced to one—Monod model and there are two models—Monod and Mink—depending on oxygen only. Separate kinetic process models have been developed for the combination of Monod–Monod and Monod–Mink models. For the first time, in addition to the multiplicative form, the additive form of a specific growth rate has been studied. The comparison of the obtained results has shown that the additive form has shown better results than the multiplicative one. For this reason, the additive form of the Monod–Monod model will be used to model the process.

From Invariance Under Binomial Thinning to Unification of the Cauchy and the Gołąb–Schinzel-Type Equations

We point out to a connection between a problem of invariance of power series families of probability distributions under binomial thinning and functional equations which generalize both the Cauchy and an additive form of the Gołąb–Schinzel equation. We solve these equations in several settings with no or mild regularity assumptions imposed on unknown functions.

FEATURES OF BREEDING VALUE INHERITANCE SIRES OF HOLSTEIN BREED

In our studies, the phenotypic manifestation of the additive form of inheritance of breeding value by milk yield (intermediate and parental dominance) was in 334 (82.2%) bulls, and non-additive form (over-dominance and regression) – in 72 (17.8%) including: over-dominance in 55 (13.5%) and regression in 17 heads (4.2%). In the population assessment, for all forms of inheritance, there was a clear quantitative shift of the breeding value of sons of milk yield to positive (+) values, compared with the breeding value of their parents. This confirms that sons, selected after their evaluation, and recognized as milk yield improvers. The variability of the breeding value of sons by milking depending on the forms of its inheritance has been established. According to the group of bulls by intermediate type of inheritance, milk yield sign were found in 291 (71.7%) sons, whose pedigree value was 606.4 ± 11.6 kg and was higher than the half-sum of both parents (554 kg), which deviates from the action of intermediate inheritance at 52 kg (109%). After all, the recognition of the intermediate nature of inheritance involves obtaining in the offspring of animals with the same set of chromosomes as their parents, and hence with the same phenotype. Therefore, from a theoretical point of view, genetic progress in the population should be not expected from this group of animals. However, in this case, the increase in breeding value was 9%, which is statistically significant (P > 0.99). A rather high variability of the breeding value of sons from its level in their parents with an intermediate form of inheritance has been established. Thus, of the 159 bulls-breeders in which the breeding value was inherited by intermediate form, only 30 sons (7.3% of the total population) of the bull Duster 2147488 (BV +579 kg and mothers with an average BV +632 kg, half the amount of the BV of both parents was +605 kg), was +605.5 ± 30.8 kg and was equal to the half-sum of the BV of both parents, and 9 (2.2%) sons of the bull Manfred 2183007, whose breeding value was, on average, at the population level +856.3 ± 37.6 kg and was equal to the half-sum of the indicator of the parents' BV (+851 kg). The inheritance of breeding value of bulls on quantitative signs of milk productivity in highly consolidated breeds on these signs, at intra-breeding selection occurs by a combination of phenotypic display of action of additive and non-additive (super-dominance) forms of inheritance. The frequency of these forms of inheritance probably is determined by the number and quality of chromosome pairs in the karyotype of animals on the probable basis of their manifestation in the population [15]. The relative variability of breeding value by milk yield along the line "father – son" and "mother – son" depends on the form of its inheritance. The coefficient of phenotypic correlation between the breeding value of parents and sons in the intermediate form of inheritance is +0.524 – +0.560 and increases with parental dominance to +0.907 ± 0.040 and +0.985 ± 0.006, and over-dominance to +0.887 ± 0.044 and +0.905 ± 0.033, at high statistical significant. Inheritance by non-additive form (over-dominance of both parents) is more effectively associated with increasing of breeding value by milk yield their sons than by the additive form.

Sistem Pendukung Keputusan terhadap Jenis dan Penerima dalam Penentuan Bantuan Desa Menggunakan Metode Simple Additive Weighting

Sidoluhur Village is a village located in Padang Jaya District, North Bengkulu which has a large population. The his village has 3 hamlets in one village. The problem in Sidoluhur Village is that it is difficult to determine the recipient of village assistance, because the number of aid proposals that are proposing is more than the number of people who receive assistance. There are so many proposals that have been submitted, this is of course very troublesome for village officials who choose to receive assistance. As problems develop, a decision support system is needed that will provide results on the computer to determine who should get help. A decision support system is a system for finding decision support, decisions are taken using a system designed based on usage needs, in helping to make decisions, decisions are designed based on predetermined criteria and alternatives and have a system that is structured and programmed in the form of weighting that will be accumulated and normalized and produce ranking. This study uses the Simple Additive weighting method, commonly referred to as a method that uses a weighted additive form. The form of the method is to calculate the total weight value of the work steps on the existing alternatives of all attributes. To explain about the completion of the method uses village aid recipient data. A lot of data that will be used as alternatives in this study are 9 candidates for village aid recipients. As a result, the recipients of aid should not be less than 0.5000, with the result that 7 recipients of assistance and 2 people who are not eligible to receive assistance.

Improved Huff Model for Estimating Urban Rail Transit Station Catchment Areas considering Station Choices

Estimating urban rail transit station catchment areas is of great significance to deepening our understanding of Transit-Oriented Development in Chinese megacities. This study investigated station choices of residents and considered that residents may not only pay attention to the proximity to stations when the URT system develops into a relatively mature network. An improved Huff model was proposed to calculate the probability of residents’ station choice, which considered the station attractiveness. The station attractiveness is measured by three variables: walk score, public transport accessibility level, and service and facility index. The additive form based on multicriteria decision is adopted to incorporate experts’ opinions on the importance of three variables. In this study, extended catchment areas that can be accessed by cycling and feeder bus services are adopted to replace the conventional pedestrian-oriented catchment areas. A case study of Xi’an, China, was used to validate the applicability of the proposed methodology. The results revealed that the methodology effectively solved the problem. The findings could be used as a reference and provide technical support to policymakers and city planners with regard to the transport facilities configuration for URT station catchment areas, which contributes to facilitating transit-oriented development.

Index for measuring convergence between objectives and practice of Islamic banking

Purpose Islamic banking was developed to serve two objectives: to replace interest-based loan system with profit and loss sharing investment modes and to promote equity in resource allocation. The first objective is called procedural whereas the second one is termed consequential. Scholars have been debating about the success of Islamic banking in achieving these objectives. This paper aims to develop an index for measuring the extent of convergence between theory and practice of Islamic banking. Design/methodology/approach For measuring the procedural and consequential convergence between objectives and practice of Islamic banking, the paper derives a set of indicators from the celebrated theory of Islamic banking and then develops the methodology of ranking all banks in terms of those indicators. Findings The paper provides ranking of Islamic banks in Pakistan in the light of this index. The results indicate that none of the Islamic banks in Pakistan has been doing good enough to achieve the convergence, instead they are moving in the opposite direction over time. Practical implications Using the methodology developed in this paper, universal ranking of Islamic banks may be issued every year. Originality/value Scholars have proposed some indices for measuring the performance of Islamic banking. There are two basic problems with these proposed measures: they do not directly compare the performance of Islamic banking against its stated objectives and they naively use an additive form of index without explaining the reason for this choice, i.e. as to what are the desirable characteristics which their preferred mathematical form of index serves. The index proposed in this paper attempts to overcome these shortcomings.

Lax Representation and Darboux Solutions of the Classical Painlevé Second Equation

In this article, we present Darboux solutions of the classical Painlevé second equation. We reexpress the classical Painlevé second Lax pair in new setting introducing gauge transformations to yield its Darboux expression in additive form. The new linear system of that equation carries similar structure as other integrable systems possess in the AKNS scheme. Finally, we generalize the Darboux transformation of the classical Painlevé second equation to the N -th form in terms of Wranskian.

A Sharp Oscillation Criterion for a Linear Differential Equation with Variable Delay

We consider linear differential equations with variable delay of the form x ′ ( t ) + p ( t ) x ( t − τ ( t ) ) = 0 , t ≥ t 0 , where p : [ t 0 , ∞ ) → [ 0 , ∞ ) and τ : [ t 0 , ∞ ) → ( 0 , ∞ ) are continuous functions, such that t − τ ( t ) → ∞ (as t → ∞ ). It is well-known that, for the oscillation of all solutions, it is necessary that B : = lim sup t → ∞ A ( t ) ≥ 1 e holds , where A : = ( t ) ∫ t − τ ( t ) t p ( s ) d s . Our main result shows that, if the function A is slowly varying at infinity (in additive form), then under mild additional assumptions on p and τ , condition B > 1 / e implies that all solutions of the above delay differential equation are oscillatory.